PP1:r(market) = 6%r(stated)=8%Par-value = 8,000,000Coupon payment = 8%*8,000,000*0.5 = 320,000Since r(market) < r(stated), investors will be willing to give us more than the par-value ofthe bonds, 8,000,000. Therefore, these bonds will sell at a premium. ProceedsPVannuity(3%,10)*320,000 + PVsa(3%,10)*8,000,000 = 8,682,464Interest expense in 2001Interest expense on June 30, 20018,682,464 * 3% = 260,474Reduction of premium after the first coupon payment is:320,000 – 260,474 = 59,526Net book value of liability = 8,682,464 – 59,526 = 8,622,938ORNet book value of liability = unamortized premium at the end + face value = (unamortized premium at the beginning – premium amortization in the current period) + face value = 682,464 – 59,526 + 8,000, 000 = 8,622, 938Interest expense on Dec 31, 2001:8,622,938 * 3% = 258,688Therefore interest expense in 2001 is:260,474 + 258,688 = 519,162Market value of bond on Dec 31, 2001PVannuity(4%, 8)*320,000 + PVsa(4%, 8)*8,000,000 = 8,000,000PP2:r(market) = 10%r(stated)=8%Par-value = 5,000,000Coupon payment = 8%*5,000,000*0.5 = 200,000Since r(market) > r(stated), investors will be willing to give us less than the par-value of the bonds, 5,000,000. Therefore, these bonds will sell at a discount. ProceedsPVannuity(5%,20)*200,000 + PVss(5%,20)*5,000,000 = 4,376,940To calculate the book value on January 1, 2008:- We can do it the long way by constructing a bond schedule. But this will take a long time…..- We can do it the easy way by thinking about what does the book value of a bond represent at any point in time.The book value is the present value of all remaining periodic payments plus the present value of the principal (par value). The present value is calculated using the historical market rate at the time of the issuance. On January 1, 2008 6 years passed, which means there are 8 payments left to be paid plus the single sum. So,BV(1/1/2008) = PVannuity(5%,8)*200,000 + PVss(5%,8)*5,000,000 = 4,676,640Note: Since the bond was issued at a discount, the book value increases over time (i.e. thediscount decreases).PP3:1. Coupon payment = 1000*8%*6/2 = 402. Interest expense for 2000 includes one period of interest expenseSale@100Interest expense = coupon payment = 40 (note: when bond is issued at par, coupon payment is equal to interest expense)Sale@96Interest expense = coupon payment + amortization of bond discount in each period = 40 + (1000-960)/(2*10) = 42 (note: when bond is issued at discount, coupon payment is less than interest expense)Sale @104Interest expense = coupon payment - amortization of bond discount in each period = 40 - (1000-960)/(2*10) = 38 (note: when bond is issued at discount, coupon payment is greater than interest expense)3. Net carrying value on Dec 31, 2001Sale@1001000 (note: when bond is issued at par, net carrying value is always equal to face value)Sale@96= face value –unamortized bond discount = 1000 – [(1000 – 960) - 3* (1000-960)/(10*2)]= 966 Sale @104face value +unamortized bond premium = 1000 + [(1040 – 1000) - 3* (1000-960)/(10*2)]=
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